PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2013 | 33 | 1 | 89-109
Tytuł artykułu

Measure valued solutions for systems governed by neutral differential equations on Banach spaces and their optimal control

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we consider the question of existence of measure valued solutions for neutral differential equations on Banach spaces when there is no mild solutions. We prove the existence of measure solutions and their regularity properties. We consider also control problems of such systems and prove existence of optimal feedback controls for some interesting a-typical control problems.
Twórcy
autor
  • University of Ottawa
Bibliografia
  • [1] H.O. Fattorini, A remark on existence of solutions of infinite dimensional noncompact optimal control problems, SIAM J. Control and Optimization 35 (4) (1997), 1422-1433. doi: 10.1137/S036301299528788X
  • [2] N.U. Ahmed, Measure solutions for semilinear evolution equations with polynomial growth and their optimal controls, Discuss. Math. Differential Inclusions 17 (1997), 5-27.
  • [3] N.U. Ahmed, Measure solutions for semilinear systems with unbounded nonlinearities, Nonlinear Analysis 35 (1998), 487-503. doi: 10.1016/S0362-546X(97)00699-8
  • [4] N.U. Ahmed, Relaxed solutions for stochastic evolution equations on Hilbert space with polynomial growth, Publicationes Mathematicae, Debrechen 54 (1-2) (1999), 75-101.
  • [5] N.U. Ahmed, Measure solutions for semilinear and quasilinear evolution equations and their optimal control, Nonlinear Analysis 40 (2000), 51-72. doi: 10.1016/S0362-546X(97)00699-8
  • [6] N.U. Ahmed, A general result on measure solutions for semilinear evolution equations, Nonlinear Analysis 42 (2000), 1335-1340. doi: 10.1016/S0362-546X(99)00145-5
  • [7] N.U. Ahmed, Deterministic and stochastic neutral systems on Banach spaces and their optimal Fedback controls, Journal of Nonlinear Systems and Applications (2009), 151-160.
  • [8] N.U. Ahmed, Measure solutions for evolution equations with discontinuous vector Fields, Nonlinear Functional Analysis & Applications 9 (3) (2004), 467-484.
  • [9] N.U. Ahmed, Optimal Stochastic Control of Measure Solutions on Hilbert Space, in Systems, Control, Modeling and Optimization (Edited by F. Ceragioli, A. Dontchev, H. Furuta, K. Marti & L. Pandolfi), Springer, (Proc. IFIP-TC7 Conference, Turin, Italy, 2005)), U.S., (2006), 1-12.
  • [10] N.U. Ahmed, Measure valued solutions for stochastic evolution equations on Hilbert space and their feedback control, Discuss. Math. Diff. Incl. Control and Optim. 25 (2005), 129-157. doi: 10.7151/dmdico.1061
  • [11] N.U. Ahmed, Measure solutions for impulsive evolution equations with measurable vector Fields, JMAA 319 (2006), 74-93.
  • [12] N. Dunford and J.T. Schwartz, Linear Operators, Part 1, Interscience Publishers, Inc., New York, 1958.
  • [13] A.N. Godunov, Peano's theorem in infinite dimensional Hilbert space is false even in a weakened formulation, Math. Zametki 15 (1974), 467-477.
  • [14] K.R. Parthasarathy, Probability Measures on Metric Spaces, Academic Press, New York and London, 1967.
  • [15] J. Dieudonné, Deaux examples déquations différentielles, Acta Sci. Math. Szeged 12B (1950), 38-40.
  • [16] O. Hernandez-Lerma and J.B. Lasserre, Cone-constrained linear equations in Banach spaces, J. Convex Analysis 4 (1) (1997), 149-164.
  • [17] B.D. Craven and J.J. Koliha, Generalization of Farkas' theorem, SIAM J. Math. Anal. 8 (6) (1977). doi: 10.1137/0508076
  • [18] N.U. Ahmed, Some Recent Developments in Systems and Control Theory on Infinite Dimensional Banach Spaces, Part 1 & 2, Proceedings of the 5th International Conference on Optimization and Control with Applications, (Edited by: K.L. Teo, H. Xu and Y. Zhang), Beijing, China, 2012; Publisher: Springer-Verlag (in Print).
  • [19] N.U. Ahmed, Optimization and Identification of Systems Governed by Evolution Equations on Banach Spaces, Pitman research Notes in Mathematics Series, 184, Longman Scientific and Technical, U.K; Co-published with John-Wiely & Sons, Inc. New York, 1988.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1142
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.